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Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e

Chapter 10

Chemical

Bonding II

Roy Kennedy

Massachusetts Bay Community College

Wellesley Hills, MA

Chemistry: A Molecular Approach, 2nd Ed.

Nivaldo Tro


Taste

• The taste of a food depends on the interaction

between the food molecules and taste cells on

your tongue

• The main factors that affect this interaction are

the shape of the molecule and charge

distribution within the molecule

• The food molecule must fit snugly into the

active site of specialized proteins on the

surface of taste cells

• When this happens, changes in the protein

structure cause a nerve signal to transmit 2 Tro: Chemistry: A Molecular Approach, 2/e


Sugar & Artificial Sweeteners

• Sugar molecules fit into the active site of taste cell

receptors called Tlr3 receptor proteins

• When the sugar molecule (the key) enters the

active site (the lock), the different subunits of the

T1r3 protein split apart

• This split causes ion channels in the cell

membrane to open, resulting in nerve signal

transmission

• Artificial sweeteners also fit into the Tlr3 receptor,

sometimes binding to it even stronger than sugar

making them “sweeter” than sugar

3 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e

Structure Determines Properties!

• Properties of molecular substances depend on the structure of the molecule

• The structure includes many factors, such as:

the skeletal arrangement of the atoms

the kind of bonding between the atoms

ionic, polar covalent, or covalent

the shape of the molecule

• Bonding theory should allow you to predict the shapes of molecules

4 Tro: Chemistry: A Molecular Approach, 2/e


Molecular Geometry • Molecules are 3-dimensional objects

• We often describe the shape of a molecule

with terms that relate to geometric figures

• These geometric figures have characteristic

“corners” that indicate the positions of the

surrounding atoms around a central atom in

the center of the geometric figure

• The geometric figures also have

characteristic angles that we call bond

angles


Lewis Theory Predicts

Electron Groups

• Lewis theory predicts there are regions of

electrons in an atom

• Some regions result from placing shared pairs

of valence electrons between bonding nuclei

• Other regions result from placing unshared

valence electrons on a single nuclei


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Using Lewis Theory to Predict

Molecular Shapes

• Lewis theory says that these regions of

electron groups should repel each other

because they are regions of negative charge

• This idea can then be extended to predict the

shapes of molecules

the position of atoms surrounding a central atom will be

determined by where the bonding electron groups are

the positions of the electron groups will be determined

by trying to minimize repulsions between them


VSEPR Theory

• Electron groups around the central atom will

be most stable when they are as far apart as

possible – we call this valence shell electron

pair repulsion theory

because electrons are negatively charged, they

should be most stable when they are separated as

much as possible

• The resulting geometric arrangement will allow

us to predict the shapes and bond angles in

the molecule


Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 9 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e

Electron Groups • The Lewis structure predicts the number of valence

electron pairs around the central atom(s)

• Each lone pair of electrons constitutes one electron

group on a central atom

• Each bond constitutes one electron group on a

central atom

regardless of whether it is single, double, or triple

O N O • • • •

• •

• •

• • • • there are three electron groups on N

three lone pair

one single bond

one double bond



Electron Group Geometry

• There are five basic arrangements of electron groups around a central atom

based on a maximum of six bonding electron groups though there may be more than six on very large atoms, it is

very rare

• Each of these five basic arrangements results in five different basic electron geometries

in order for the molecular shape and bond angles to be a “perfect” geometric figure, all the electron groups must be bonds and all the bonds must be equivalent

• For molecules that exhibit resonance, it doesn’t matter which resonance form you use – the electron geometry will be the same


Linear Electron Geometry

• When there are two electron groups around the

central atom, they will occupy positions on

opposite sides of the central atom

• This results in the electron groups taking a linear

geometry

• The bond angle is 180°


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Linear Geometry


Trigonal Planar Electron Geometry

• When there are three electron groups around the central atom, they will occupy positions in the shape of a triangle around the central atom

• This results in the electron groups taking a trigonal planar geometry




Trigonal Geometry


Tetrahedral Electron Geometry

• When there are four electron groups around the

central atom, they will occupy positions in the

shape of a tetrahedron around the central atom

• This results in the electron groups taking a

tetrahedral geometry

• The bond angle is 109.5°



Tetrahedral Geometry


Trigonal Bipyramidal Electron Geometry

• When there are five electron groups around the central

atom, they will occupy positions in the shape of two

tetrahedra that are base-to-base with the central atom in the

center of the shared bases

• This results in the electron groups taking a trigonal

bipyramidal geometry

• The positions above and below the central atom are called

the axial positions

• The positions in the same base plane as the central atom

are called the equatorial positions

• The bond angle between equatorial positions is 120°

• The bond angle between axial and equatorial positions is 90°


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Trigonal Bipyramid


Trigonal Bipyramidal Geometry



Octahedral Electron Geometry

• When there are six electron groups around the central

atom, they will occupy positions in the shape of two

square-base pyramids that are base-to-base with the

central atom in the center of the shared bases

• This results in the electron groups taking an octahedral

geometry

it is called octahedral because the geometric figure has

eight sides

• All positions are equivalent




Octahedral Geometry


Octahedral Geometry


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Molecular Geometry • The actual geometry of the molecule may be

different from the electron geometry

• When the electron groups are attached to

atoms of different size, or when the bonding to

one atom is different than the bonding to

another, this will affect the molecular geometry

around the central atom

• Lone pairs also affect the molecular geometry

they occupy space on the central atom, but are not

“seen” as points on the molecular geometry



Not Quite Perfect Geometry

Because the bonds and

atom sizes are not

identical in formaldehyde,

the observed angles are

slightly different from ideal


The Effect of Lone Pairs

• Lone pair groups “occupy more space” on the

central atom

because their electron density is exclusively on the

central atom rather than shared like bonding electron

groups

• Relative sizes of repulsive force interactions is

Lone Pair – Lone Pair > Lone Pair – Bonding Pair > Bonding Pair – Bonding Pair

• This affects the bond angles, making the bonding

pair – bonding pair angles smaller than expected



Effect of Lone Pairs

The bonding electrons are shared by two

atoms, so some of the negative charge is

removed from the central atom

The nonbonding electrons are localized on

the central atom, so area of negative charge

takes more space


Bond Angle Distortion

from Lone Pairs


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Bond Angle Distortion

from Lone Pairs


Bent Molecular Geometry:

Derivative of Trigonal Planar Electron Geometry

• When there are three electron groups around

the central atom, and one of them is a lone pair,

the resulting shape of the molecule is called a

trigonal planar — bent shape

• The bond angle is less than 120°

because the lone pair takes up more space



Pyramidal & Bent Molecular Geometries:

Derivatives of Tetrahedral Electron Geometry • When there are four electron groups around the

central atom, and one is a lone pair, the result is called a pyramidal shape

because it is a triangular-base pyramid with the central atom at the apex

• When there are four electron groups around the central atom, and two are lone pairs, the result is called a tetrahedral—bent shape

it is planar

it looks similar to the trigonal planar—bent shape, except the angles are smaller

• For both shapes, the bond angle is less than 109.5°


Methane



Pyramidal Shape


Pyramidal Shape


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Tetrahedral–Bent Shape


Tetrahedral–Bent Shape



Derivatives of the

Trigonal Bipyramidal Electron Geometry

• When there are five electron groups around the central atom, and some are lone pairs, they will occupy the equatorial positions because there is more room

• When there are five electron groups around the central atom, and one is a lone pair, the result is called the seesaw shape aka distorted tetrahedron

• When there are five electron groups around the central atom, and two are lone pairs, the result is called the T-shaped

• When there are five electron groups around the central atom, and three are lone pairs, the result is a linear shape

• The bond angles between equatorial positions are less than 120°

• The bond angles between axial and equatorial positions are less than 90° linear = 180° axial–to–axial


Replacing Atoms with Lone Pairs

in the Trigonal Bipyramid System



Seesaw Shape


T–Shape


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T–Shape


Linear Shape



Derivatives of the

Octahedral Geometry • When there are six electron groups around the

central atom, and some are lone pairs, each even number lone pair will take a position opposite the previous lone pair

• When there are six electron groups around the central atom, and one is a lone pair, the result is called a square pyramid shape the bond angles between axial and equatorial positions is

less than 90°

• When there are six electron groups around the central atom, and two are lone pairs, the result is called a square planar shape the bond angles between equatorial positions is 90°


Square Pyramidal Shape



Square Planar Shape

47 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 48 Tro: Chemistry: A Molecular Approach, 2/e

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Predicting the Shapes

Around Central Atoms

1. Draw the Lewis structure

2. Determine the number of electron groups

around the central atom

3. Classify each electron group as bonding or

lone pair, and count each type

remember, multiple bonds count as one group

4. Use Table 10.1 to determine the shape and

bond angles


Example 10.2: Predict the geometry and bond

angles of PCl3

1. Draw the Lewis

structure

a) 26 valence electrons

2. Determine the

Number of electron

groups around

central atom

a) four electron groups

around P



Example 10.2: Predict the geometry and bond

angles of PCl3

3. Classify the electron groups

a) three bonding groups

b) one lone pair

4. Use Table 10.1 to determine the

shape and bond angles

a) four electron groups around P =

tetrahedral electron geometry

b) three bonding + one lone pair =

trigonal pyramidal molecular

geometry

c) trigonal pyramidal = bond angles

less than 109.5° 51 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e

Practice – Predict the molecular geometry

and bond angles in SiF5−




and bond angles in SiF5─

Si = 4e─

F5 = 5(7e─) = 35e─

(─) = 1e─

total = 40e─

5 electron groups on Si

5 bonding groups

0 lone pairs

Shape = trigonal bipyramid

Bond angles

Feq–Si–Feq = 120°

Feq–Si–Fax = 90°

Si least electronegative

Si is central atom



and bond angles in ClO2F


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and bond angles in ClO2F

Cl = 7e─

O2 = 2(6e─) = 12e─

F = 7e─

Total = 26e─

4 electron groups on Cl

3 bonding groups

1 lone pair

Shape = trigonal pyramidal

Bond angles

O–Cl–O < 109.5°

O–Cl–F < 109.5°

Cl least electronegative

Cl is central atom


Representing 3-Dimensional Shapes

on a 2-Dimensional Surface

• One of the problems with drawing molecules is

trying to show their dimensionality

• By convention, the central atom is put in the plane

of the paper

• Put as many other atoms as possible in the same

plane and indicate with a straight line

• For atoms in front of the plane, use a solid wedge

• For atoms behind the plane, use a hashed wedge



SF6

S

F

F

F

F F

F



H O

| ||

H C C O H

|

H

Multiple Central Atoms • Many molecules have larger structures with many

interior atoms

• We can think of them as having multiple central

atoms

• When this occurs, we describe the shape around

each central atom in sequence

shape around left C is tetrahedral

shape around center C is trigonal planar

shape around right O is tetrahedral-bent


Describing the Geometry

of Methanol


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Describing the Geometry

of Glycine


Practice – Predict the molecular geometries

in H3BO3



3 electron groups on B

B has

3 bonding groups

0 pone pairs

4 electron groups on O

O has

2 bonding groups

2 lone pairs

Practice – Predict the molecular geometries

in H3BO3

B = 3e─

O3 = 3(6e─) = 18e─

H3 = 3(1e─) = 3e─

Total = 24e─ Shape on B = trigonal planar

B least electronegative

B Is Central Atom

oxyacid, so H attached to O

Shape on O = tetrahedral bent


Polarity of Molecules


• For a molecule to be polar it must

1. have polar bonds

electronegativity difference - theory

bond dipole moments - measured

2. have an unsymmetrical shape

vector addition

• Polarity affects the intermolecular forces of

attraction

therefore boiling points and solubilities

like dissolves like

• Nonbonding pairs affect molecular polarity,

strong pull in its direction


Molecule Polarity

The H─Cl bond is polar. The bonding

electrons are pulled toward the Cl end of

the molecule. The net result is a polar

molecule.


Vector Addition


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Molecule Polarity

The O─C bond is polar. The bonding

electrons are pulled equally toward both

O ends of the molecule. The net result is

a nonpolar molecule.



Molecule Polarity

The H─O bond is polar. Both sets of

bonding electrons are pulled toward the

O end of the molecule. The net result

is a polar molecule.


Predicting Polarity of Molecules

1. Draw the Lewis structure and determine the

molecular geometry

2. Determine whether the bonds in the molecule

are polar

a) if there are not polar bonds, the molecule is

nonpolar

3. Determine whether the polar bonds add

together to give a net dipole moment



Example 10.5: Predict whether NH3 is a

polar molecule

1. Draw the Lewis

structure and

determine the

molecular geometry

a) eight valence electrons

b) three bonding + one lone

pair = trigonal pyramidal

molecular geometry



polar molecule

2. Determine if the bonds

are polar

a) electronegativity

difference

b) if the bonds are not polar,

we can stop here and

declare the molecule will

be nonpolar

ENN = 3.0

ENH = 2.1

3.0 − 2.1 = 0.9

therefore the

bonds are

polar covalent


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polar molecule

3) Determine whether the polar bonds add together to give a net dipole moment

a) vector addition

b) generally, asymmetric

shapes result in

uncompensated

polarities and a net

dipole moment

The H─N bond is polar. All

the sets of bonding

electrons are pulled toward

the N end of the molecule.

The net result is a polar

molecule.


Practice – Decide whether the following

molecules are polar

EN

O = 3.5

N = 3.0

Cl = 3.0

S = 2.5



Practice – Decide whether the following

molecules Are polar

polar nonpolar

1. polar bonds, N-O

2. asymmetrical shape 1. polar bonds, all S-O

2. symmetrical shape

Trigonal

Bent Trigonal

Planar

2.5


Molecular Polarity

Affects

Solubility in Water

• Polar molecules are attracted

to other polar molecules

• Because water is a polar

molecule, other polar

molecules dissolve well in

water

and ionic compounds as well

• Some molecules have both

polar and nonpolar parts 76 Tro: Chemistry: A Molecular Approach, 2/e


Problems with Lewis Theory • Lewis theory generally predicts trends in

properties, but does not give good numerical predictions

e.g. bond strength and bond length

• Lewis theory gives good first approximations of the bond angles in molecules, but usually cannot be used to get the actual angle

• Lewis theory cannot write one correct structure for many molecules where resonance is important

• Lewis theory often does not predict the correct magnetic behavior of molecules

e.g. O2 is paramagnetic, though the Lewis structure predicts it is diamagnetic


Valence Bond Theory

• Linus Pauling and others applied the principles

of quantum mechanics to molecules

• They reasoned that bonds between atoms

would occur when the orbitals on those atoms

interacted to make a bond

• The kind of interaction depends on whether the

orbitals align along the axis between the

nuclei, or outside the axis


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Orbital Interaction • As two atoms approached, the half-filled

valence atomic orbitals on each atom would

interact to form molecular orbitals

molecular orbtials are regions of high probability of

finding the shared electrons in the molecule

• The molecular orbitals would be more stable

than the separate atomic orbitals because they

would contain paired electrons shared by both

atoms

the potential energy is lowered when the molecular

orbitals contain a total of two paired electrons

compared to separate one electron atomic orbitals 79 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e

Orbital Diagram for the

Formation of H2S

+

↑

H

1s ↑↓ H─S bond

↑

H

1s

S ↑ ↑ ↑↓ ↑↓

3s 3p

↑↓ H─S bond

Predicts bond angle = 90°

Actual bond angle = 92°



Valence Bond Theory – Hybridization • One of the issues that arises is that the number

of partially filled or empty atomic orbitals did not predict the number of bonds or orientation of bonds

C = 2s22px12py

12pz0 would predict two or three

bonds that are 90° apart, rather than four bonds that are 109.5° apart

• To adjust for these inconsistencies, it was postulated that the valence atomic orbitals could hybridize before bonding took place one hybridization of C is to mix all the 2s and 2p

orbitals to get four orbitals that point at the corners of a tetrahedron


Unhybridized C Orbitals Predict the

Wrong Bonding & Geometry



Valence Bond Theory

Main Concepts 1. The valence electrons of the atoms in a

molecule reside in quantum-mechanical atomic

orbitals. The orbitals can be the standard s, p,

d, and f orbitals, or they may be hybrid

combinations of these.

2. A chemical bond results when these atomic

orbitals interact and there is a total of two

electrons in the new molecular orbital

a) the electrons must be spin paired

3. The shape of the molecule is determined by the geometry of the interacting orbitals


Hybridization

• Some atoms hybridize their orbitals to

maximize bonding

• more bonds = more full orbitals = more stability

• Hybridizing is mixing different types of orbitals

in the valence shell to make a new set of

degenerate orbitals

sp, sp2, sp3, sp3d, sp3d2

• Same type of atom can have different types of

hybridization

C = sp, sp2, sp3


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Hybrid Orbitals

• The number of standard atomic orbitals combined = the number of hybrid orbitals formed combining a 2s with a 2p gives two 2sp hybrid

orbitals

H cannot hybridize!! its valence shell only has one orbital

• The number and type of standard atomic orbitals combined determines the shape of the hybrid orbitals

• The particular kind of hybridization that occurs is the one that yields the lowest overall energy for the molecule


Carbon Hybridizations

Unhybridized

2s 2p

sp hybridized

2sp

sp2 hybridized

2p

sp3 hybridized

2p

2sp2

2sp3



sp3 Hybridization

• Atom with four electron groups around it

tetrahedral geometry

109.5° angles between hybrid orbitals

• Atom uses hybrid orbitals for all bonds and

lone pairs



Orbital Diagram of the

sp3 Hybridization of C


sp3 Hybridized Atoms

Orbital Diagrams

Unhybridized atom

2s 2p

sp3 hybridized atom

2sp3

C

2s 2p

2sp3

N

• Place electrons into hybrid and unhybridized valence orbitals

as if all the orbitals have equal energy

• Lone pairs generally occupy hybrid orbitals


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Practice – Draw the orbital diagram for

the sp3 hybridization of each atom

Unhybridized atom

3s 3p

Cl

2s 2p

O

sp3 hybridized atom

3sp3

2sp3


Bonding with Valence Bond Theory

• According to valence bond theory, bonding

takes place between atoms when their atomic

or hybrid orbitals interact

“overlap”

• To interact, the orbitals must either be aligned

along the axis between the atoms, or

• The orbitals must be parallel to each other and

perpendicular to the interatomic axis



Methane Formation with sp3 C


Ammonia Formation with sp3 N



Types of Bonds

• A sigma (s) bond results when the interacting atomic orbitals point along the axis connecting the two bonding nuclei

either standard atomic orbitals or hybrids s–to–s, p–to–p, hybrid–to–hybrid, s–to–hybrid, etc.

• A pi (p) bond results when the bonding atomic orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei

between unhybridized parallel p orbitals

• The interaction between parallel orbitals is not as strong as between orbitals that point at each other; therefore s bonds are stronger than p bonds


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Orbital Diagrams of Bonding

• “Overlap” between a hybrid orbital on one atom

with a hybrid or nonhybridized orbital on

another atom results in a s bond

• “Overlap” between unhybridized p orbitals on

bonded atoms results in a p bond


CH3NH2 Orbital Diagram

sp3 C sp3 N

1s H

s

s s s s s

1s H 1s H 1s H 1s H

H C

H

H

N H

H

··s s

s s

s

s



Formaldehyde, CH2O Orbital Diagram

sp2 C

sp2 O

1s H

s

s s

1s H

p C p O p


sp2

• Atom with three electron groups around it

trigonal planar system C = trigonal planar

N = trigonal bent

O = “linear”

120° bond angles

flat

• Atom uses hybrid orbitals for s bonds and lone pairs, uses nonhybridized p orbital for p bond



sp2 Hybridized Atoms

Orbital Diagrams

Unhybridized atom

2s 2p

sp2 hybridized atom

2sp2

2p

C

3 s

1 p

2s 2p

2sp2

2p

N

2 s

1 p


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Practice – Draw the orbital diagram for

the sp2 hybridization of each atom. How many s

and p bonds would you expect each to form?

Unhybridized atom

2s 2p

B

3 s

0 p

2s 2p

O

1 s

1 p

sp2 hybridized atom

2sp2

2p

2sp2

2p


Hybrid orbitals

overlap to form a

s bond.

Unhybridized p

orbitals overlap

to form a p bond.



CH2NH Orbital Diagram

sp2 C

sp2 N

1s H

s

s s s

1s H 1s H

p C p N p

105

C N

H

H H

Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e

Bond Rotation

• Because the orbitals that form the s bond point

along the internuclear axis, rotation around

that bond does not require breaking the

interaction between the orbitals

• But the orbitals that form the p bond interact

above and below the internuclear axis, so

rotation around the axis requires the breaking

of the interaction between the orbitals


Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 107 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 108 Tro: Chemistry: A Molecular Approach, 2/e

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sp • Atom with two electron groups

linear shape

180° bond angle

• Atom uses hybrid orbitals for s bonds or lone

pairs, uses nonhybridized p orbitals for p bonds

p

p

s



sp Hybridized Atoms

Orbital Diagrams

Unhybridized atom

2s 2p

sp hybridized atom

2sp

2p

C

2s

2p

2s 2p

2sp

2p

N

1s

2p



HCN Orbital Diagram

sp C

sp N

1s H

s

s

p C p N 2p


sp3d • Atom with five electron groups

around it

trigonal bipyramid electron geometry

Seesaw, T–Shape, Linear

120° & 90° bond angles

• Use empty d orbitals from valence shell

• d orbitals can be used to make p bonds


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sp3d Hybridized Atoms

Orbital Diagrams

Unhybridized atom

3s 3p

sp3d hybridized atom

3sp3d

S

3s 3p

3sp3d

P

3d

3d

(non-hybridizing d orbitals not shown)



SOF4 Orbital Diagram

sp3d S

sp2 O

2p F

s

s

d S p O p

2p F

s

2p F

s

2p F

s


sp3d2

• Atom with six electron groups

around it

octahedral electron geometry

Square Pyramid, Square Planar

90° bond angles

• Use empty d orbitals from

valence shell to form hybrid

• d orbitals can be used to make

p bonds



sp3d2 Hybridized Atoms

Orbital Diagrams

Unhybridized atom sp3d2 hybridized atom

S

3s 3p 3sp3d2

↑↓

3d

↑↓ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

I

5s 5p

↑↓

5d

↑↓ ↑↓ ↑

5sp3d2

↑↓ ↑ ↑ ↑ ↑ ↑

(non-hybridizing d orbitals not shown)


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Predicting Hybridization and

Bonding Scheme

1. Start by drawing the Lewis structure

2. Use VSEPR Theory to predict the electron group

geometry around each central atom

3. Use Table 10.3 to select the hybridization

scheme that matches the electron group

geometry

4. Sketch the atomic and hybrid orbitals on the

atoms in the molecule, showing overlap of the

appropriate orbitals

5. Label the bonds as s or p



Example 10.7: Predict the hybridization

and bonding scheme for CH3CHO

123

Draw the Lewis structure

Predict the electron group

geometry around inside

atoms

C1 = 4 electron areas

C1= tetrahedral

C2 = 3 electron areas

C2 = trigonal planar




124

Determine the

hybridization of the

interior atoms

C1 = tetrahedral

C1 = sp3

C2 = trigonal planar

C2 = sp2

Sketch the molecule and

orbitals

Tro: Chemistry: A Molecular Approach, 2/e


Label the bonds




Practice – Predict the hybridization of all

the atoms in H3BO3

H = can’t hybridize

B = 3 electron groups = sp2

O = 4 electron groups = sp3


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Practice – Predict the hybridization and

bonding scheme of all the atoms in NClO

N = 3 electron groups = sp2

O = 3 electron groups = sp2

Cl = 4 electron groups = sp3

• • O N C l • •

• •

• • • • • •

127

Cl

O Ns:Nsp2─Clp

Cl

O N

s:Osp2─Nsp2

p:Op─Np

↑↓

↑↓

↑↓ ↑↓

↑↓

↑↓


Problems with Valence Bond Theory

• VB theory predicts many properties better than

Lewis theory

bonding schemes, bond strengths, bond lengths,

bond rigidity

• However, there are still many properties of

molecules it doesn’t predict perfectly

magnetic behavior of O2

• In addition, VB theory presumes the electrons

are localized in orbitals on the atoms in the

molecule – it doesn’t account for delocalization



Molecular Orbital Theory • In MO theory, we apply Schrödinger’s wave

equation to the molecule to calculate a set of

molecular orbitals

in practice, the equation solution is estimated

we start with good guesses from our experience as to

what the orbital should look like

then test and tweak the estimate until the energy of the

orbital is minimized

• In this treatment, the electrons belong to the

whole molecule – so the orbitals belong to the

whole molecule

delocalization


LCAO

• The simplest guess starts with the atomic

orbitals of the atoms adding together to make

molecular orbitals – this is called the Linear

Combination of Atomic Orbitals method

weighted sum

• Because the orbitals are wave functions, the

waves can combine either constructively or

destructively



Molecular Orbitals

• When the wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals – it is called a Bonding Molecular Orbital

s, p

most of the electron density between the nuclei

• When the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbitals – it is called an Antibonding Molecular Orbital

s*, p*

most of the electron density outside the nuclei

nodes between nuclei


Interaction of 1s Orbitals


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Molecular Orbital Theory

• Electrons in bonding MOs are stabilizing

lower energy than the atomic orbitals

• Electrons in antibonding MOs are

destabilizing

higher in energy than atomic orbitals

electron density located outside the

internuclear axis

electrons in antibonding orbitals cancel

stability gained by electrons in bonding orbitals


Energy Comparisons of Atomic Orbitals

to Molecular Orbitals



MO and Properties

• Bond Order = difference between number of

electrons in bonding and antibonding orbitals

only need to consider valence electrons

may be a fraction

higher bond order = stronger and shorter bonds

if bond order = 0, then bond is unstable compared to

individual atoms and no bond will form

• A substance will be paramagnetic if its MO

diagram has unpaired electrons

if all electrons paired it is diamagnetic


1s 1s

s*

s

Hydrogen

Atomic

Orbital

Hydrogen

Atomic

Orbital

Dihydrogen, H2

Molecular

Orbitals

Because more electrons are in

bonding orbitals than are in antibonding orbitals,

net bonding interaction



H2

s* Antibonding MO

LUMO s bonding MO

HOMO


1s 1s

s*

s

Helium

Atomic

Orbital

Helium

Atomic

Orbital

Dihelium, He2

Molecular

Orbitals

Because there are as many electrons in

antibonding orbitals as in bonding orbitals,

there is no net bonding interaction

BO = ½(2-2) = 0


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1s 1s

s*

s

Lithium

Atomic

Orbitals

Lithium

Atomic

Orbitals

Dilithium, Li2

Molecular

Orbitals

Because more electrons are

in bonding orbitals than are in

antibonding orbitals, there is a

net bonding interaction

2s 2s

s*

s Any fill energy level will

generate filled bonding

and antibonding MO’s;

therefore only need to

consider valence shell

BO = ½(4-2) = 1


s bonding MO

HOMO

s* Antibonding MO

LUMO

Li2



Interaction of p Orbitals


Interaction of p Orbitals



O2

• Dioxygen is paramagnetic

• Paramagnetic material has unpaired electrons

• Neither Lewis theory nor valence bond theory predict this result


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O2 as Described by Lewis and

VB Theory


Oxygen

Atomic

Orbitals

Oxygen

Atomic

Orbitals

2s 2s

2p 2p

s*

s

s*

s

p*

p Because more electrons

are in bonding orbitals

than are in antibonding

orbitals, there is a net

bonding interaction

Because there are unpaired

electrons in the

antibonding orbitals,

O2 is predicted to be

paramagnetic

O2 MO’s

BO = ½(8 be – 4 abe)

BO = 2



N has 5 valence

electrons

2 N = 10e−

(−) = 1e−

total = 11e−

Example 10.10: Draw a molecular orbital diagram

of N2− ion and predict its bond order and magnetic

properties

147

Write a MO

diagram for N2−

using N2 as a

base

Count the

number of

valence

electrons and

assign these to

the MOs

following the

aufbau

principle, Pauli

principle &

Hund’s rule ↑ ↓ s2s

s*2s

p2p

s2p

p*2p

s*2p

↑ ↓

↑ ↑ ↓ ↓

↑ ↓

↑


Example 10.10: Draw a molecular orbital diagram

of N2− ion and predict its bond order and magnetic

properties

148

Calculate the

bond order by

taking the

number of

bonding

electrons and

subtracting the

number of

antibonding

electrons, then

dividing by 2

Determine

whether the ion

is paramagnetic

or diamagnetic ↑ ↓ s2s

s*2s

p2p

s2p

p*2p

s*2p

↑ ↓

↑ ↑ ↓ ↓

↑ ↓

↑

BO = ½(8 be – 3 abe)

BO = 2.5

Because this is lower

than the bond order

in N2, the bond

should be weaker

Because there

are unpaired

electrons, this ion

is paramagnetic



Practice – Draw a molecular orbital diagram of C2+

and predict its bond order and magnetic properties

149 Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e 150

↑ ↓ s2s

s*2s

p2p

s2p

p*2p

s*2p

↑ ↓

↑ ↑ ↓

BO = ½(5 be – 2 abe)

BO = 1.5

Because there

are unpaired

electrons, this ion

is paramagnetic

Practice – Draw a molecular orbital diagram of C2+

and predict its bond order and magnetic properties

C has 4 valence

electrons

2 C = 8e−

(+) = −1e−

total = 7e−


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Heteronuclear Diatomic Molecules & Ions

• When the combining atomic orbitals are

identical and equal energy, the contribution of

each atomic orbital to the molecular orbital is

equal

• When the combining atomic orbitals are

different types and energies, the atomic

orbital closest in energy to the molecular

orbital contributes more to the molecular

orbital


Heteronuclear Diatomic Molecules & Ions

• The more electronegative an atom is, the

lower in energy are its orbitals

• Lower energy atomic orbitals contribute

more to the bonding MOs

• Higher energy atomic orbitals contribute

more to the antibonding MOs

• Nonbonding MOs remain localized on the

atom donating its atomic orbitals



NO

a free radical

s2s Bonding MO

shows more

electron density

near O because

it is mostly O’s

2s atomic orbital

153

BO = ½(6 be – 1 abe)

BO = 2.5


HF



Polyatomic Molecules

• When many atoms are combined together, the

atomic orbitals of all the atoms are combined to

make a set of molecular orbitals, which are

delocalized over the entire molecule

• Gives results that better match real molecule

properties than either Lewis or valence bond

theories


Ozone, O3

156

MO Theory:

Delocalized

p bonding

orbital of O3


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